The use of a subsurface annulus safety valve for installation between inner and outer concentric tubular members such as a well tubing and a well casing and for opening and closing the annulus is well known as shown in U.S. Pat. Nos. 4,049,052 and 4,273,194. However, while prior annulus safety valves were secured to or connected to the inner tubular member or tubing, they were merely sealed against the outer tubular member or casing by an integral seal or by a well packer. That is, the annulus safety valve was not locked to the outer tubular member such as the casing. However, it is important to have the annulus safety valves releasably locked to the outer member for insuring the control of the well. In the event of a failure, such as the loss of a wellhead, high pressures below the packer would allow the tubing, and all safety valves connected thereto to be blown out of the well.